% macros
\def\figwidth{0.95\columnwidth}

% abbreviations
\def\fig{Fig.~}
\def\figs{Figs.~}
\def\sec{Sec.~}

% latin
\def\eg{{e.g.}}
\def\ie{{i.e.}}
\def\apriori{\emph{a priori}}

% From http://www.f.kth.se/~ante/latex.php#marginpar
\setlength{\marginparwidth}{.75in}
\let\oldmarginpar\marginpar
\renewcommand\marginpar[1]{\-\oldmarginpar[\raggedleft\footnotesize #1]%
{\raggedright\footnotesize #1}}

% My own custom todo highligher
\newcommand\Todo{\textcolor{magenta}{\textbf{Todo}}}


% math
%\newcommand{\vect}[1]{\vec{#1}}
%\renewcommand{\vec}[1]{\mathbf{#1}}
\newcommand{\Fourier}{\mathscr{F}}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\Cov}{Cov}
\DeclareMathOperator{\corr}{corr}
\DeclareMathOperator{\cov}{cov}
\DeclareMathOperator{\var}{var}
% Some math commands
\DeclareMathOperator{\sinc}{sinc}
\DeclareMathOperator{\Toeplitz}{Toeplitz}
\DeclareMathOperator{\conj}{conj}
\DeclareMathOperator{\rank}{rank}

\DeclareMathOperator{\argmax}{arg\,max}
\DeclareMathOperator{\argsubmax}{arg\,submax}
\DeclareMathOperator{\submax}{submax}

\newcommand{\argmin}{\operatornamewithlimits{arg~min}}
\newcommand{\abs}[1]{\left|#1\right|}
\newcommand{\C}{\ensuremath{\mathbb{C}}}
\newcommand{\R}{\ensuremath{\mathbb{R}}}
\def\vphi{{\bm{\phi}}}
\def\vlambda{{\bm{\lambda}}}
\def\vs{\vec{s}}
\def\mK{\vec{K}}
\def\vm{\vec{m}}
\def\mU{\vec{U}}
\def\mL{{\bm{\Lambda}}}
\newcommand{\SINR}[1]{\text{SINR}\left(#1\right)}
\newcommand{\Exp}[1]{E\left\lbrace#1\right\rbrace}
\newcommand{\smallExp}[1]{E\lbrace#1\rbrace}

\newcommand{\bigbrace}[1]{\left\lbrace#1\right\rbrace}

%\renewcommand{\vec}[1]{\mathbf{#1}}
\def\mI{\vec{I}}
\def\vg{\vec{g}}
%\def\vmu{\vec{\mu}}
\def\vn{\vec{n}}
\def\vchi{\vec{\chi}}


%VARIABLE LIST
%--------------------------------------------------------------------------------
\def\t{{t}}                    %time
\def\SpaceLoc{{L}}             %Spatial Location (of an antenna)
%\def\Fourier{{}}              %Fourier transform (already exist)

\def\TimeIdx{{m}}              %Time index 
\def\NTimeIdx{{N_m}}           %Number of time indecies 
\def\RecAnten{{R}}             %list of receivers antennas
\def\RecAntenIdx{{q}}          %Index for list of receivers antennas
\def\RecAntenIdxed{\RecAnten_{\RecAntenIdx}}         %Indexed list of receivers antennas
\def\NRecAnten{{N_R}}          %Number of receivers
\def\TranAnten{{T}}            %list of transmitting antennas
\def\TranAntenIdx{{s}}         %Index for list of transmitting antennas
\def\TranAntenIdxed{\TranAnten_{\TranAntenIdx}}      %Indexed list of transmitting antennas
\def\NTranAnten{{N_T}}         %Number of transmitters
\def\Freq{{f}}                 %list of frequncies
\def\FreqIdx{{k}}              %Index for list of frequncies
\def\FreqIdxed{\Freq_{\FreqIdx}}                      %Indexed list of frequncies
\def\NFreq{{N_f}}              %Number of receivers


\def\AmpCRBModel{{G}}          %Amplitude
\def\Phase{{\psi}}             %Phase
\def\PRI{{\tau}}               %Pulse Repetition Interval

\def\xLoc{{x}}                 %x location
\def\velx{\dot{x}}             %x velocity
\def\accelx{\ddot{x}}          %x acceleration
\def\yLoc{{y}}                 %y location
\def\vely{\dot{y}}             %y velocity
\def\accely{\ddot{y}}          %y acceleration

\def\AzAngle{{\theta}}         %Azimuth Angle
\def\ElAngle{{\phi}}           %Elivation Angle

\def\WGnoise{{\epsilon}}       %White Gaussian noise
\def\vWGnoise{\vec{\epsilon}}  %White Gaussian noise

\def\Px{{P_x}}                 %Projection operation for x component
\def\Py{{P_y}}                 %Projection operation for y component

\def\k{{k}}                    %Variable for kspace
 \def\vk{\vec{k}}              %vector of kspace variables
%\def\PhaseHist{{g}}            %element of phase history
\def\vPhaseHist{\vec{g}}       %Vector containing all phase history
%\def\CNChi{{\chi}}             %Compressed Notation chi exponentials of phase history
\def\vCNChi{\vec{\chi}}        %Compressed Notation chi exponentials of phase history

\def\Data{\vec{y}}             %measured data of regression problem
\def\Lendata{{M}}             %number of measured data of regression problem
\def\Image{\vec{x}}            %image of regression proble
\def\LenImage{{N}}            %number of points in the image of regression proble
\def\ForwardOp{{A}}            %Forward operator of regression problem

\def\ModOrder{{L}}             %Model order for the result of the sparse regression problem
\def\EstImageAmp{{\alpha}}     %Estimate of the amplitude of an image element
\def\EstImageFreq{{f}}         %Estimate of the frequncy of an image element
\def\NdicElem{{N}}             %Number of dictionary elements
\def\p{{p}}                    %p of the p norm

\def\Nva{{N_{va}}}             %Number of velocity acceleration slices
\def\VAPhaseErr{{\Psi}}        %Phase offsets due to velocity and acceleration
\def\VAPhaseErrIdx{{u}}   %Index for v-a slice of Phase offsets due to velocity and acceleration
\def\VAPhaseErrIdx{\VAPhaseErr_{\VAPhaseErrIdx}}      %Indexed v-a slice of Phase offsets due to v-a
\def\ImageOp{{\Fourier}}       %Image operator
\def\NgridPtsX{{U}}            %Number of grid points in the x direction (for sparse recon)
\def\NgridPtsY{{V}}            %Number of grid points in the y direction (for sparse recon)

\def\MVNmean{{\mu}}            %mean of a multivariate normal distribution
\def\MNVcov{{\Sigma}}          %Covariance matrix of a multivariate normal distribution
\def\Unknows{{\Theta}}         %vector of unknowns to be estimated
\def\CRB{{C}}                  %CRB
\def\FIM{{F}}                  %Fisher Information Matrix

\def\CostSparseRecon{{J}}      %Cost function for sparse reconstruction problem
\def\ImageLinOp{{D}}           %Linear Operation applied to Image before p norm penalty
\def\ImageLinOpIdx{{i}}       %Index for linear Operation applied to Image before p norm penalty
\def\ImageLinOpIdxed{\ImageLinOp_{\ImageLinOpIdx}}    %Indexed linear Operation applied to Image before p norm penalty
\def\NImageLinOp{{N_D}}       %Linear Operation applied to Image before p norm penalty
\def\PnormParam{{\lambda}}     %parameter for the p norm penalty

\def\AppxHessian{{H}}          %Approximation to the hessian matrix
\def\GNiteration{{\kappa}}     %Iteration of Gauss Newton step
\def\GNstepSize{{\gamma}}      %Step size of Gauss Newton process
\def\PDinvData{{b}}            %Positive Definite matrix inversion "Data" (Right Hand Side)
\def\PDinvMatrix{{H}}          %Positive Definite matrix inversion Matrix
\def\PDinvImage{{a}}           %Positive Definite matrix inversion "Image" (Left Hand Side)

\def\CGResidual{{r}}           %Conjugate Gradiant residual for Positive Definite matrix inversion
\def\CGstepDirection{{d}}      %Step Direction of Conjugate gradiant process
\def\CGstepSize{{\varsigma}}   %Compressed Notation
%--------------------------------------------------------------------------------


\newcommand{\partheta}[2]{\frac{\partial{#1}}{\partial{\Theta_{#2}}}}

\newcommand{\parA}[1]{\frac{\partial{#1}}{\partial{\AmpCRBModel}}}
\newcommand{\parp}[1]{\frac{\partial{#1}}{\partial{\Phase}}}
\newcommand{\parx}[1]{\frac{\partial{#1}}{\partial{\xLoc_0}}}
\newcommand{\pary}[1]{\frac{\partial{#1}}{\partial{\yLoc_0}}}
\newcommand{\parvx}[1]{\frac{\partial{#1}}{\partial{\velx_0}}}
\newcommand{\parvy}[1]{\frac{\partial{#1}}{\partial{\vely_0}}}
\newcommand{\parax}[1]{\frac{\partial{#1}}{\partial{\accelx}}}
\newcommand{\paray}[1]{\frac{\partial{#1}}{\partial{\accely}}}
%\newcommand{\FIMrow}[4]{ \chi_{{#1},{#2},{#3}}({#4}T)&  A\chi_{{#1},{#2},{#3}}({#4}T)j&  
%            A\chi_{{#1},{#2},{#3}}({#4}T)j\frac{4\pi f_{{#3}}}{c}Px_{{#1},{#2}}({#4}T)&
%            A\chi_{{#1},{#2},{#3}}({#4}T)j\frac{4\pi f_{{#3}}}{c}Py_{{#1},{#2}}({#4}T)&
%            A\chi_{{#1},{#2},{#3}}({#4}T)j\frac{4\pi f_{{#3}}}{c}t Pvx_{{#1},{#2}}({#4}T)&
%            A\chi_{{#1},{#2},{#3}}({#4}T)j\frac{4\pi f_{{#3}}}{c}t Pvy_{{#1},{#2}}({#4}T) }




% EOF
